Problem: Complete the recursive formula of the geometric sequence $500\,,\,200\,,\,80\,,\,32,...$. $c(1)=$
Explanation: The first term is $500$ and the common ratio is $\dfrac25$. ${\times\dfrac25\,\curvearrowright}$ ${\times\dfrac25\,\curvearrowright}$ ${\times\dfrac25\,\curvearrowright}$ $500,$ $200,$ $80,$ $32,...$ This is the recursive formula of $500\,,\,200\,,\,80\,,\,32,...$. $\begin{cases} c(1)=500 \\\\ c(n)=c(n-1)\cdot\dfrac25 \end{cases}$